How can I configure blender to import a custom mesh from the shift + a add mesh menu?
An existing solution
There is the Asset Flinger Add-on which might be interesting to you.

(....) Free Blender Add-on for simple mesh importing via graphical menu. It's aimed at 3D modellers who constantly import pre-made 3D assets from their libraries for building their highly detailed creations.
The Add-on also includes a drag-and-drop thumbnail generator for .obj files for Windows and Linux (....)

Make your assets, save them as .obj and go through the instructions for making thumbnails. All instructions can be found on that link.